Separate distinct internal closed volume (automated)
You could try adding the Solidify modifier, boosting Thickness a bit, and then hitting Apply. Then, go to edit mode, select a vertex, and do Select Linked All to select a particular volume. Finally, choose Separate (P key by default) to move the selected volume into its own object.

Your topology will have to be well organized to start I think (i.e. faces don't intersect each other) otherwise the 'solidified' topology will be weird too.